Angle gathers in wave-equation imaging for transversely isotropic media

Conclusions

We have developed analytical relationships to generate angle gathers using wave-equation migration in VTI media. These relations are based on an approach for generating gathers at each depth level by converting offset-space-frequency planes into angle-space planes while simultaneously applying the imaging condition. Although the angle gathers depend on medium parameters, they are independent of the structure, which provides an opportunity for a simple and practical implementation. Comparing the mapping equation for VTI media with those for the isotropic case demonstrates the large influence that the anisotropy parameter $\eta$ has on the mapping process. On the other hand, the influence of vertical velocity is confined to the offset direction, and the influence of NMO velocity is small. Synthetic data applications demonstrate the importance of accurate mapping of energy in the angle domain. In the case of a TTI medium, the required modification to the mapping equations is given by the transformation of the wavenumbers in the dispersion relation to the direction of of the symmetry axis and, as a result, a similar analytic mapping exists.

Angle gathers in wave-equation imaging for transversely isotropic media